D-optimum designs for the linear logistic model when restrictions exist on p

Suppose that the linear logistic model describes the relationship between a proportion p and some quantitative variable x and that p varies within the range [ p 01, p 02]⊂[0,1]. Using the Karush-Kuhn-Tucker theorem, the D-optimum design for this model is a balanced 2-point design with the location o...

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Bibliographic Details
Published inJournal of statistical planning and inference Vol. 37; no. 2; pp. 255 - 264
Main Authors Scazzero, Joseph A., Ord, J.K.
Format Journal Article
LanguageEnglish
Published Lausanne Elsevier B.V 01.11.1993
New York,NY Elsevier Science
Amsterdam
Subjects
D-optimality
Exact sciences and technology
Experimental design
logistic regression
Mathematics
Probability and statistics
Quality assurance
Sciences and techniques of general use
Statistics
D-optimality
Quality assurance
Primary 62K05
logistic regression
secondary 62N10
Logistic regression
Optimality criterion
Efficiency
Linear model
Optimal design
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Summary:Suppose that the linear logistic model describes the relationship between a proportion p and some quantitative variable x and that p varies within the range [ p 01, p 02]⊂[0,1]. Using the Karush-Kuhn-Tucker theorem, the D-optimum design for this model is a balanced 2-point design with the location of the design points determined by p 01, p 02. A step-by-step procedure is presented for obtaining the D-optimum design points for any values p 01, p 02. In addition, the efficiencies of these designs are discussed in the context of quality assurance experiments.
ISSN:0378-3758
1873-1171
DOI:10.1016/0378-3758(93)90094-M